L'estimation des modes d'une densité de probabilité multidimensionnelle

Jean-Pierre Asselin de Beauville

Statistique et analyse des données (1983)

  • Volume: 8, Issue: 3, page 16-40
  • ISSN: 0750-7364

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Asselin de Beauville, Jean-Pierre. "L'estimation des modes d'une densité de probabilité multidimensionnelle." Statistique et analyse des données 8.3 (1983): 16-40. <http://eudml.org/doc/108899>.

@article{AsselindeBeauville1983,
author = {Asselin de Beauville, Jean-Pierre},
journal = {Statistique et analyse des données},
keywords = {algorithm; almost sure convergence; mode estimation; estimating model sets; histogram-type estimator; moving density threshold},
language = {fre},
number = {3},
pages = {16-40},
publisher = {Association pour la statistique et ses illustrations},
title = {L'estimation des modes d'une densité de probabilité multidimensionnelle},
url = {http://eudml.org/doc/108899},
volume = {8},
year = {1983},
}

TY - JOUR
AU - Asselin de Beauville, Jean-Pierre
TI - L'estimation des modes d'une densité de probabilité multidimensionnelle
JO - Statistique et analyse des données
PY - 1983
PB - Association pour la statistique et ses illustrations
VL - 8
IS - 3
SP - 16
EP - 40
LA - fre
KW - algorithm; almost sure convergence; mode estimation; estimating model sets; histogram-type estimator; moving density threshold
UR - http://eudml.org/doc/108899
ER -

References

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  1. 1 J.P. ASSELIN de BEAUVILLE : "Un algorithme d'estimation du mode Etude de la convergence". Pub. Inst. Stat. Univ. Paris, 1979, XXIV, fasc. 3-4, p. 1-29. Zbl0426.62018MR561814
  2. 2 E. PARZEN : "On estimation of a probability density function and mode". Ann. Math. Statist. (1962), 33, p. 1065-1076. Zbl0116.11302MR143282
  3. 3 H. CHERNOFF : "Estimation of the mode". Ann. Inst. Statist. Math. (1964), 16, p. 31-41. Zbl0212.21802MR172382
  4. 4 E.A. NADARAYA : "On non parametric estimates of density function and regression curves". Theor. Probability Appl. (1965), 10, p. 186-190. Zbl0134.36302MR172400
  5. 5 T. DALENIUS : "The mode. A neglected statistical parameter". J. Roy. Statist. Soc. (1965), Ser. A, 128, p. 110-11 MR185720
  6. 6 U. GRENANDER : "Some direct estimates of the mode". Ann. Math. Statist. (1965), 36, p. 131-138. Zbl0131.17702MR170409
  7. 7 J.H. VENTER : "On estimation of the mode". Ann. Math. Statist. (1967), 38, p. 1446-1455. Zbl0245.62033MR216698
  8. 8 B.P. LIENTZ : "Results on non parametric modal intervale". SIAM Journal on Applied Math. (1970), 19, p. 355 366. Zbl0207.18703MR266382
  9. 9 E.J. WEGMAN : "A note on the estimation of the mode". Ann. Math. Statist. (1971), 42, 6, p. 1909-1915. Zbl0227.62028MR297072
  10. 10 H. EKBL0M : "A Monte-Carlo investigation of mode estimators in samples". Appl. Statist. (1972), 21, 2, p. 177-184. 
  11. 11 J. FRITZ : "Stochastic approximation for finding local maxima o probability densities". Studia Scientiarium Mathematicarum Hungarica (1973), p. 309-322. Zbl0288.60028MR351003
  12. 12 T. ROBERTSON et J.D. CRYER : "An iterative procedure for estima the mode". J.A.S.A. (1974), 69, 348, p. 1012-1016. Zbl0301.62015MR431499
  13. 13 T.W. SAGER : "Consistency in non parametric estimation of the mode". Ann. Statist. (1975), 3, p. 698-706. Zbl0303.62037MR373142
  14. 14 W.F. EDDY : "Optimum kernel estimators of the mode". Ann. Statist. (1980), 8, 4, p. 870-882. Zbl0438.62027MR572631
  15. 15 M. SAMANTA : "Nonparametric estimation of the mode of a multivariate density". S. Afr. Statist. J. (1973) , 7, p. 109-117. Zbl0268.62015MR331618
  16. 16 V.D. KONAROV : "On the asymptotic normality of the mode of multidimensional distributions". Theor. Probability Appl. (1974), 19, p. 794-799. Zbl0325.62033
  17. 17 T.W. SAGER : "Estimation of a multivariate mode". Ann. Statist. (1978), 6, p. 802-812. Zbl0378.62037MR491553
  18. 18 T.W. SAGER : "An iterative method for estimating a multivariate mode and isopleth". J.A.S.A. (1979), 74, 366, p. 329-339. Zbl0428.62040MR548023
  19. 19 T. CACOULLOS : "Estimation of a multivariate density". Ann. Inst. Statist. Math. (1966), 10, p. 179-189. Zbl0202.49603MR210255
  20. 20 D. WISHART : "Mode analysis : A generalisation of nearest neighbour which reduces chaining effects". Numerical Takonomy (1969), ed. A.J. COIE, Academic Press, London, p. 282-311. 
  21. 21 D. WISHART : "Numerical classification method for deriving natural classes". Nature (1969), 221, 4, p. 97-98. 
  22. 22 I. GITMAN et M.D. LEVINE : "An algorithm for detecting unimodal fuzzy sets and its application as a clustering technique". IEEE Trans. Comput. (1970), C-19, p. 583-593. Zbl0194.48101
  23. 23 I. GITMAN : "An algorithm for nonsupervised pattern classification". IEEE trans. system man, cybern. (1973), SMC-3, 1, p. 66-74. Zbl0245.68043
  24. 24 D.J. EIGEN, F.R. FROMM, R.A. NORTHOUSE : "Cluster analysis based on dimensional information with applications to feature selection and classification". IEEE trans. System, man, cybern. (1974), SMC-4, 3. Zbl0305.68073
  25. 25 R. MIZOGUCHI et M. SHIMURA : "Nonparametric learning without a teacher based on mode estimation". IEEE Trans. Comput. (1976), C-25, 11. Zbl0354.68117MR428848
  26. 26 J.A. HARTIGAN : "Clustering algorithms". (1975), Ed. Wiley. Zbl0372.62040MR405726
  27. 27 J.A. HARTIGAN : "Clusters as modes". First International Symposium on date analysis and informatics (1977), IRIA, p. 433-448. 
  28. 28 C. VASSEUR et J. POSTAIRE : "Convexité des fonctions de densité : Application à la détection des modes en reconnaissance des formes". RAIRO Automatique (1979), 13, 2, p. 171-188. Zbl0411.93032MR537655
  29. 29 C. VASSEUR et J. POSTAIRE : "A convexity testing method for cluster analysis". IEEE Trans. Syst. Man. Cybern. (1980), SMC-10, 3. Zbl0438.62050MR567188
  30. 30 R.S. CHHIKARA et D.T. REGISTER : "A numerical classification method for partitioning of large multidimensional mixed data set". Technometrics, (1979), 21, 4, p. 531-537. 
  31. 31 R.M. CORMACK : "A review of classification". J. Roy. Statist. Soc., (1971), A, 134, p. 321-367. Zbl0446.62052MR448716
  32. 32 H.H. BOCK : "Clustering by density estimation". Analyse des Données et Informatique (1979), INRIA, p. 173-186. Zbl0446.62061
  33. 33 M. LIMOURI et J. POSTAIRE : "Utilisation des histogrammes unidimensionnels en classification automatique". Reconnaissance des formes et intelligence artificielle (1979), AFCET-IRIA, p. 373-380. 
  34. 34 J. KIEFER et J. WOLFOWITZ : "On the deviations of the empiric distribution function of vector chance variables". Trans. Am. Math. Soc. (1958), 87, p. 173-186. Zbl0088.11305MR99075
  35. 35 M. BERTRANS-RETALI : "Convergence uriforme stochastique d'un estimateur d'une densité de probabilité dans RS". C.R. Acad. Sc. (1974), A, 278, p. 451-453. Zbl0275.62031MR331615
  36. 36 P. REVESZ : "Testing of density functions". Periods. Math. Hungar. (1971), 1, p. 35-44. Zbl0222.62015MR290495
  37. 37 P. REVESZ : "On empirical density functions". Periods. Math. Hungar. (1972), 2, p. 85-110. Zbl0246.62063MR368287
  38. 38 P. REVESZ : "A strong law of the empirical density function". Transactions sixth Prague Conf. (1973). Prague, p. 747-753. Zbl0282.62014MR362680

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